Question

A vessel of volume 100ml contains 10% oxygen and 90% unknown gas. The gas is diffuse in 86 seconds through a small hole of vessel if pure oxygen diffuse in 75 sec. Find molecular weight of unknown gas.

Answer 1

Graham's law of diffusiuon says -- the rate of diffusion of a gas is inversely proportional to the square root of it’s density or molecular weights. If r1 and r2 are the rates of diffusion of two gases, whose densities under the given conditions are d1 and d2 respectively, then we have

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where M2and M1 are the molecular weights of the gases.

NOW , here molecular weight of oxygen = 32

Let the molecular weight of gas be M , average molecular weight of gas mixture = (10*32 + 90 *M) /100 = 3.2 + .9 * M

Applying above law ,

roxygen / rmixture = (Mmixture /Moxygen)1/2

86/75 =( 3.2+ .9 *M / 32)1/2

solving we get = 43.19 gm